CASSEGRAIN REFLECTOR WITH CORRECTED FIELD. 43 



Now && = %k, 3& = ; and if by figuring or otherwise we annul coma, so that 

 G = 0, we have 



Also 

 so that 



also K = kj(f = ku/v ; so that the curvature is 



lv ...... (21) 



If we compare this with the expression given in (20) above we see that the sole 

 effect of the change is to replace the reciprocal of the focal length of the second 

 mirror by (2/c + ir) for the reverser, and, since its factor in u, v is small, this change 

 will not allow any considerable modification of the curvature of the field. 



To meet the difficulty of curvature SCHWARZSCHILD considers a design of instrument 

 fundamentally altered. Thus in (19) the curvature of the field will vanish if 



K = -v/u a {l+ K (-u+v)} 



and this may be secured if K' is negative as well as K, or if the second mirror is concave ; 

 but in order that the curvature of the mirror may not be too great we must then 

 take I+K( u + v) sensibly different from zero, and also v/u the magnification of the 

 second mirror, not too large. The system to which SCHWARZSCHILD is led as 

 generally the best to be found under such conditions has been already described 

 (p. 28). It is so different from anything that has yet been made that it must be 

 regarded merely as an interesting exploration of the possibilities of the theory until 

 an attempt is made to realise it. In particular it is utterly different from the long- 

 focus Cassegrain which I have in mind, and therefore I shall not require to refer 

 to it further. 



Returning to the question of the Cassegrain proper we see that if an improvement 

 is to be made it must be by inserting a corrector of some form in the course of the 

 beam. Hence we come to the system which I have indicated on p. 29. To get an 

 approximation to what is required, suppose that the reverser is merely a convex 

 mirror, that the corrector consists of a pair of thin lenses of which the theory is given 

 on pp. 37 and 38, and that all the surfaces are spherical except that of the great 

 mirror which is figured so as to annul spherical aberration. To fix ideas I shall 

 suppose that the unit of length is 100 inches, and that with this unit the aperture of 

 the great mirror is 0'40 and its focal length 2'0000, also that the separation of the two 

 mirrors is 1'3333, that the magnification of the second mirror is 2 '4, from which it 

 results that its focal length is l/'875 = T1429, and the principal focus of the combina- 

 tion is thrown beyond the great mirror by '2667, at a distance T6000 from the 



a 2 



